It is therefore convenient to apply a transformation from moments to canonical
coordinates. Such a transformation always exists locally according to the
Darboux theorem [1]} or its extension to Poisson manifolds
[2]}. To second order for a single classical degree of freedom,
canonical coordinates for the moments \(\Delta (q^2)\) , \(\Delta (qp)\)  and
\(\Delta (p^2)\)  are given by \((s,p_s)\)  such that
[3]}, [4]}, [5]}
\( \Delta (q^2) = s^2 \quad ,\quad \Delta (qp)=sp_s \quad ,\quad \Delta (p^2)=p_s^2+\frac{U}{s^2}\) 
